A323350 Nonprime numbers > 1 whose number of prime factors counted with multiplicity is a perfect square.

16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376

Offset

1,1

Comments

First differs from A014613 in having 512.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

360 = 2*2*2*3*3*5 has 6 prime factors, and 6 is not a perfect square, so 360 does not belong to the sequence.
2160 = 2*2*2*2*3*3*3*5 has 8 prime factors, and 8 is not a perfect square, so 2160 does not belong to the sequence.
10800 = 2*2*2*2*3*3*3*5*5 has 9 prime factors, and 9 is a perfect square, so 10800 belongs to the sequence.

Maple

filter:= proc(n) local t;
  t:= numtheory:-bigomega(n);
  t > 1 and issqr(t)
end proc:
select(filter, [$4..1000]); # Robert Israel, Jan 15 2019

Mathematica

Select[Range[100], #>1&&!PrimeQ[#]&&IntegerQ[Sqrt[PrimeOmega[#]]]&]

Prog

(PARI) isok(n) = (n>1) && !isprime(n) && issquare(bigomega(n)); \\ Michel Marcus, Jan 15 2019

Crossrefs

Cf. A000005, A001222, A063989, A067028, A067340, A070175, A071625, A118914, A167175, A323305.

Sequence in context: A067028 A110893 A014613 * A307341 A046370 A376704

Adjacent sequences: A323347 A323348 A323349 * A323351 A323352 A323353

Keyword

nonn

Author

Gus Wiseman, Jan 15 2019

Status

approved